Geometry Regents High School Examination

Exam Instructions

• No communication devices allowed.
• Required tools: graphing calculator, straightedge, and compass.
• Examination consists of 4 parts, with 35 questions.
• Answers for Part I must be recorded on a separate answer sheet.
• Use pen for all work except graphs/drawings (use pencil).
• Indicate all necessary steps for solutions.
• Formulas provided at the end, and a sheet of scrap graph paper is available.

Exam Format

• Part I: 24 questions, 2 credits each, multiple-choice format.
• Part II: 7 questions, 2 credits each, show work for full credit.
• Part III: 3 questions, 4 credits each, show work for full credit.
• Part IV: 1 question, 6 credits, show work for full credit.

Part I Sample Questions

1. Dilation and Scale Factor: Determine the scale factor and center of dilation mapping triangle nABC to nAB'C'.
2. Line Segment Division: Calculate coordinates of point A dividing segment PAQ in a 2:3 ratio.
3. Transformation Sequence: Identify the sequence of transformations mapping parallelogram ABCD onto RSTU.
4. Trigonometry in Triangles: Calculate side length AB in a right triangle ABC.
5. Proving Triangle Congruence: Determine which additional statement proves triangles PQR and LMN congruent.
6. Circle Equation: Find the center and radius of the given circle equation.
7. 3D Rotation: Identify the 3D object formed by rotating a square.
8. Perpendicular Lines: Find equation of a line perpendicular to a given line through a specific point.
9. Triangle Medians: Analyze properties of median in triangle JKL.
10. Circle Chord and Angle Calculation: Find angle measure given intersecting chords.
11. Triangle Area Calculation: Calculate area of triangle ABC from graph coordinates.

Part II Sample Questions

25. Angle Measurement: Determine the measure of angle D in a quadrilateral mapping problem.
26. Segment Construction: Use compass and straightedge to construct a segment 1/4 the length of segment AB.
27. Trigonometry Application: Calculate height of a bird above ground based on angle of elevation.
28. Density and Volume Calculation: Determine mass of a silver charm.
29. Triangle Similarity Proof: Prove triangles ADE and ABC are similar.

Part III Sample Questions

32. Land Measurement Problem: Use right triangle properties to determine angle between surveyor and land features.
33. Volume Calculation in Prisms: Calculate volume of topsoil needed for garden bed and cost of topsoil.
34. Triangle Proportionality: Prove a ratio involving triangle sides using given information.

Part IV Sample Question

35. Triangle and Rectangle Proofs: Prove triangle PET is a right triangle and prove PENT is a rectangle using coordinates and transformations.

Reference Sheet

• Includes geometric formulas, Pythagorean theorem, quadratic formula, sequences, and conversions.